The chemical structures of the three complexes (left) and the optimized structures (right) at the LSDA/SDD level are shown in Figure 1 . The optimized data of bond length and bond angle are shown in Table 1 . The optimized bond lengths of the Pt-Cl are 2.342 Å (Pt(bipy)Cl₄), 2.340 Å (Pt(en)Cl₄), and 2.339 Å (Pt(dach)Cl₄) in Table 1 . The Cl-Pt-Cl bond angle (from small to large) is Pt(bipy)Cl₄ (89.060°) < Pt(dach)Cl₄ (95.747°) < Pt(en)Cl₄ (95.980°). Ju Guang Han (1) et al. proved that the longer the bond length of Pt-Cl, the weaker the binding ability between them and Cl, which means that it is easier to break the binding between Pt and Cl in the presence of a DNA/protein environment. Afterwards, Pt(IV) is easier to reduce to Pt (II) to exert anticancer activity. The calculated result shows that the optimized bond lengths of Pt-Cl are 2.342 Å (Pt(bipy)Cl₄), 2.340 Å (Pt(en)Cl), and 2.339 Å (Pt(dach)Cl₄). The order is Pt(bipy)Cl₄ > Pt(en)Cl₄ > Pt(dach)Cl₄, which means that Pt(bipy)Cl₄ is most easily reduced and Pt(dach)Cl₄ is the most difficult to reduce. The experimental value of R(Pt-Cl1) is 2.33 Å. The deviations are 0.012 Å (Pt(bipy)Cl₄), 0.009 Å (Pt(dach)Cl₄), and 0.01 Å (Pt(en)Cl₄). The experimental value of R(Pt-N1) is 2.17 Å. The deviations are 0.161 Å (Pt(bipy)Cl₄), 0.13 Å (Pt(dach)Cl₄), and 0.119 Å (Pt(en)Cl₄). The bond lengths of Pt-Cl and Pt-N obtained by calculation are close to the experimental values (16). In addition, the intensity of the interaction between Pt and Cl is also a sign that the detachment rate of Cl^- from complex in some way in a DNA/protein environment. This is also a method of measuring reaction kinetics that bind Pt(IV) anticancer drugs to DNA (1).

Experiments have shown that the reactivity of these three complexes with glutathione (GSH), L-cysteine (L-Cys), and L-methionine (L-Met) follows this rule: Pt(bipy)Cl₄ > Pt(dach)Cl₄ > Pt(en)Cl₄ (29). The order of the Pt-N bond length (from short to long) and the Cl-Pt-Cl bond angle (from small to large) is Pt(bipy)Cl₄ < Pt(dach)Cl₄ < Pt(en)Cl₄, which is just the opposite of the reactivity order proved by experiments (29). However, the order of the bond angles of Cl-Pt-N (from large to small) is Pt(bipy)Cl₄ > Pt(dach)Cl₄ > Pt(en)Cl₄, which is the same as the reactivity order proved by experiments. Thus, we could infer that the bond length of Pt-N from short to long and the bond angle of Cl-Pt-Cl from small to large are negatively correlated with the reactivity. The bond angle of Cl-Pt-N from large to small is positively correlated with the reactivity.

We calculated the IR frequencies and intensities of Pt(dach)Cl₄, Pt(bipy)Cl₄, and Pt(en)Cl₄ at the LSDA/SDD level. The calculated infrared spectra of these complexes and the experimental infrared spectra of ammonium confirm the characteristic tetrachloroplatinate (Chemical Database of Chinese Academy of Sciences) are depicted in Figure 2 . The calculated and experimental data are shown in Table 2 . The vibration types exhibited by the highest peaks of these three complexes are the out-of-plane bending vibrations of C-H and N-H: γ(CH) and γ(NH) are at 779 cm^-1 in Pt(bipy)Cl₄, γ(CH) and γ(NH) are at 1,122 cm^-1 in Pt(dach)Cl₄, and γ(CH) and γ(NH) are at 1,088 cm^-1 in Pt(en)Cl₄, and Pt(en)Cl₄ has the highest infrared intensity. By comparing Pt(dach)Cl₄ and Pt(en)Cl₄, we can clearly find that the highest peak of Pt(bipy)Cl₄ shifts to the low-frequency region. Moreover, CH-related vibration types include in-plane bending vibration [δ(CH)] and symmetric stretching vibration [υ(CH)]. The position of δ(CH) is at 1,471 cm^-1 in Pt(bipy)Cl₄, 1,560 cm^-1 in Pt(dach)Cl₄, and 1,585 cm^-1 in Pt(en)Cl₄, and Pt(bipy)Cl₄ has the highest infrared spectral intensity and shifts to low frequency. The position of υ(CH) is at 3,098 cm^-1 in Pt(bipy)Cl₄, 3,363 cm^-1 in Pt(dach)Cl₄, and 3,416 cm^-1 in Pt(en)Cl₄, and Pt(en)Cl₄ has the highest infrared spectral intensity. In addition, the absorption peak of Pt(bipy)Cl₄ shifts obviously to the low-frequency region compared with Pt(en)Cl₄.

We observe that the vibration types related to Pt are symmetric stretching vibration [υ_sym(Cl-Pt-Cl)], antisymmetric stretching vibration [υ_asym(Cl-Pt-Cl)], scissoring vibration [scr(Cl-Pt-Cl)], and out-of-plane bending vibration [γ(Cl-Pt-Cl)]. The position of υ_sym(Cl-Pt-Cl) is at 374 cm^-1 in Pt(bipy)Cl₄, 375 cm^-1 in Pt(dach)Cl₄, and 376 cm^-1 in Pt(en)Cl₄, and Pt(bipy)Cl₄ has the highest infrared intensity. The position of υ_asym(Cl-Pt-Cl) is at 360 cm^-1 in Pt(bipy)Cl₄, 365 cm^-1 in Pt(dach)Cl₄, and 357 cm^-1 in Pt(en)Cl₄, and Pt(dach)Cl₄ has the highest infrared intensity. The position of γ(Cl-Pt-Cl) is at 122 cm^-1 in Pt(bipy)Cl₄, 135 cm^-1 in Pt(dach)Cl₄, and 145 cm^-1 in Pt(en)Cl₄, and Pt(en)Cl₄ has the highest infrared intensity. In addition, compared with Pt(en)Cl₄, the absorption peak of Pt(bipy)Cl₄ shifts slightly to the low-frequency region. The position of scr(Cl-Pt-Cl) is at 162 cm^-1 in Pt(bipy)Cl₄, 94 cm^-1 in Pt(dach)Cl₄, and 112 cm^-1 in Pt(en)Cl₄, and Pt(bipy)Cl₄ has the highest infrared intensity. In addition, compared with Pt(bipy)Cl₄, the absorption peak of Pt(dach)Cl₄ shifts obviously to the low-frequency region.

The infrared spectrum of ammonium tetrachloroplatinate has three peaks between 300 cm^-1 and 3,500 cm^-1, and the vibration modes are in-plane bending vibration [δ(CH)], symmetric stretching vibration [υ(CH)], and symmetric stretching vibration [υ_sym(Cl-Pt-Cl)]. Ammonium tetrachloroplatinate, Pt(bipy)Cl₄, Pt(dach)Cl₄, and Pt(en)Cl₄ have similar structures. The positions of δ(CH), υ_sym(Cl-Pt-Cl), and υ(CH) are 1,401 cm^-1, 3,163 cm^-1, and 325 cm^-1, respectively, in ammonium tetrachloroplatinate. Compared with the experimental results, the smaller the substituent attached to Pt, the more the positions of δ(CH) and υ_sym(Cl-Pt-Cl) move to the high-frequency region. The size of the substituent does not affect the position of υ(CH).

The HOMO–LUMO gap values play a vital role in a wide range of chemical interactions (30). The size of HOMO and LUMO shows the ability to lose and gain electrons. The energy gap is an important stability index for the individual species concerned (31, 32). Generally speaking, a large HOMO–LUMO gap indicates high stability. High stability of a molecule reflects low reducibility toward chemical reactions in some sense. A small HOMO–LUMO gap indicates that the overall energy difference between the occupied and non-occupied orbits is smaller. The smaller overall energy difference lends smaller excitation energy and larger polarizability (33). The HOMO–LUMO gap values are calculated at the LSDA/SDD level. The different physical parameters calculated from HOMO–LUMO are displayed in Table 3 . The HOMO and LUMO of three complexes are displayed in Figure 3 .

The HOMO–LUMO gap of Pt(bipy)Cl₄, Pt(en)Cl₄, and Pt(dach)Cl₄ are 1.68699 eV, 2.05500 eV, and 2.11760 eV, respectively. Thus, the order of polarizability from large to small is Pt(bipy)Cl₄ > Pt(en)Cl₄ > Pt(dach)Cl₄, the order of stability from large to small is Pt(dach)Cl₄ > Pt(en)Cl₄ > Pt(bipy)Cl₄, and the order of reducibility from large to small is Pt(bipy)Cl₄ > Pt(en)Cl₄ > Pt(dach)Cl₄. Ju Guang Han (1) et al. proved that low electron affinity leads to poor ability to obtain electrons; thus, the stability is strong. The electron affinity of Pt(bipy)Cl₄, Pt(en)Cl₄, and Pt(dach)Cl₄ are 4.81490 kcal mol^-1, 4.66676 kcal mol^-1, and 4.47491 kcal mol^-1, respectively; hence, order of stability from large to small is Pt(dach)Cl₄ > Pt(en)Cl₄ > Pt(bipy)Cl₄. Therefore, the rules of the HOMO–LUMO gap and electron affinity proved that Pt(bipy)Cl₄ has the largest reducibility and Pt(dach)Cl₄ has the smallest reducibility. The order of softness from large to small is Pt(bipy)Cl₄ (1.18554) > Pt(dach)Cl₄ (1.08494) > Pt(en)Cl₄ (0.97324). Softness reflects the activity of electrons and the degree of deformation of their distribution. Generally speaking, the larger the softness indicates, the easier it is for a molecule to react. Thus, softness also shows that Pt(bipy)Cl₄ is more responsive than Pt(dach)Cl₄.

Mulliken atomic charge calculation is a vital function in the application of quantum chemical calculation, because it affects physical properties such as electronic structures, molecular polarizability, and many other properties of a molecular system (34, 35). Natural charge analysis is an alternative to the traditional Mulliken population analysis. It shows better numerical stability and better description of the electron distribution in complexes with high ionic properties, such as complexes containing metal atoms (36).

The calculated natural charges of Pt(bipy)Cl₄, Pt(dach)Cl₄, and Pt(en)Cl₄ at the LSDA/SDD level are displayed in Tables 4 – 6 . Natural charge distribution histograms are shown in Figure 4 . Among the three complexes, Cl and N connected to Pt are negatively charged. In the four Cl substituents of Pt(bipy)Cl₄, Cl22 and Cl25 have a high amount of charge (−0.017 a.u.) while the lowest charge is seen on Cl23 (−0.034 a.u.). In the four Cl substituents of Pt(dach)Cl₄, Cl22 and Cl25 have a high amount of charge (−0.016 a.u.) while the lowest charge is seen on Cl23 and Cl21 (−0.049 a.u.). In the four Cl substituents of Pt(en)Cl₄, Cl15 and Cl16 have a high amount of charge (−0.020 a.u.) while the lowest charge is seen on Cl14 and Cl17 (−0.055 a.u.).

Ju Guang Han et al. proved that the more charge Pt carries, the greater the activity (1). The dose required to inhibit tumor is inversely related to Pt activity. Pt(bipy)Cl₄ carries the most charge (−0.569 a.u.), so it has the highest activity and the minimum dose required for the treatment of tumors. Pt(dach)Cl₄ carries the least charge (−0.772 a.u.), so it has the lowest activity and the largest dose required for tumor treatment. The cytotoxicity carried by anticancer Pt complexes is related to the Cl atomic charge. The smaller the negative charge is, the smaller the toxicity is (1). Pt(bipy)Cl₄ is the least toxic (−0.101 a.u.) and Pt(dach)Cl₄ is more toxic (−0.13 a.u.) than Pt(bipy)Cl₄. Pt(bipy)Cl₄ is better than Pt(dach)Cl₄ in terms of toxicity and dose of the drug needed to treat cancer; thus, we infer that Pt(bipy)Cl₄ has a greater potential in the treatment of cancer.

NBO analysis provides an effective method for studying intramolecular bonds, intermolecular bonds, and bond–bond interactions. It also provides a convenient basis for studying charge transfer or conjugate interactions in molecular systems (37). The second-order Fork matrix is used to evaluate the donor–acceptor interactions in NBO analysis (38). The interactions result in a loss of occupancy from the localized NBO of the idealized Lewis structure into an empty non-Lewis orbital. (39) The electron donor orbit (i), electron acceptor orbit (j), and the corresponding second-order stabilization energy distribution [E⁽²⁾] in the stable configurations of the three complexes are shown in Tables 7 – 9 . The E⁽²⁾ value represents the degree (strong or weak) of electron delocalization and the interaction between electron donor and electron acceptor, which show the contribution tendency of the electrons transferring from electron donor to the electron acceptor (40).

The largest interaction energies of the three complexes appear between the anti-bonding donor and the anti-bonding acceptor, showing great delocalization effects. The largest interaction energy is the anti-bonding N11-Pt13 and anti-bonding N12-Pt13 in the Pt(bipy)Cl₄ complex (6,875.43 kcal/mol). This result clearly demonstrates strong delocalization between BD*(1)N11-Pt13 and BD*(1)N12-Pt13, and also shows a large tendency of anti-bonding N11-Pt13 to provide electrons to anti-bonding N12-Pt13. The interactions between the central atom Pt and the surrounding atoms are BD*(1)Pt16-Cl21 to BD*(1)N14-Pt16 and BD*(1)Pt13-Cl17 to BD*(1)N10-Pt13, and their energies are 2,135.53 kcal/mol and 912.87 kcal/mol, respectively, in the Pt(dach)Cl₄ and Pt(dach)Cl₄ complex. According to the comparison of calculated data, the degree of electron delocalization between the anti-bonding donor and the anti-bonding acceptor of Pt(bipy)Cl₄ is higher than that of Pt(dach)Cl₄ and Pt(en)Cl₄.

The ODI of an orbit is calculated by this formula (41):

Where Θ _A,i ′ is the composition of atom A in orbital i.

The delocalization degree of orbit means that the range of orbit distribution is narrow or wide. The larger the distribution range, the stronger the delocalization (42). The ODI is a useful indicator of quantifying the extent of orbital spatial delocalization. The lower (higher) the ODI is, the stronger the orbital delocalization (localization) is. For example, if an orbit is completely localized on an atom, the orbital component of that atom is 100%. Then, the ODI value is (100²)/100 = 100, which reaches the theoretical maximum. If this orbit is evenly distributed on two atoms, the ODI value will be (50² + 50²)/100 = 50, which is obviously smaller. Strong delocalization indicates that orbits occupy more atoms; thus, the ODI value will be small (41). We calculate the ODI of Pt(dach)Cl₄, Pt(bipy)Cl₄, and Pt(en)Cl₄ through the Mulliken and Hirshfeld methods at the LSDA/SDD level. The calculation process was completed using the Multiwfn 3.8 software, and the obtained data are shown in Table 10 . Figure 5 shows the orbital isosurface map of the partial orbitals of three complexes.

By comparing the ODI values and orbital isosurface maps, it can be seen that the ODI value is indeed able to quantify the extent of orbital delocalization faithfully. HOMO 84, HOMO 74, and HOMO 60 show a partial delocalization character. Four Cl ions connected by the central Pt atom of each complex mainly and equally contribute to the orbital; therefore, their ODI is not quite high (41). Comparing the data obtained using the Mulliken method, the ODI of Pt(bipy)Cl₄ is smallest in the three complexes (HOMO 84 = 24.91, LUMO 85 = 10.28). Comparing the data obtained using the Hirshfeld method, the ODI of Pt(bipy)Cl₄ is smallest in the three complexes (HOMO 84 = 23.72, LUMO 85 = 8.01). Therefore, the HOMO and LUMO orbitals of Pt(bipy)Cl₄ have strong delocalization.

Molecular electrostatic potential is defined as the energy needed to transfer positive charges from an infinite distance to a point in the space around the molecule. Bonaccorsi et al. (43) first defined the electrostatic potential energy of molecules:

where Z and R represent the charge and position of the nucleus, respectively, and r represents the distance of a unit positive charge from a molecule that produces an electrostatic field (44). The molecular electrostatic potential is widely used to predict molecular nucleophilic sites, nucleophilic sites, and molecular recognition modes.

The molecular surface electrostatic potential can be expressed by a three-dimensional electrostatic potential diagram. The three-dimensional electrostatic potential diagram of the three complexes at the LSDA/SDD level is shown in Figure 6 . The molecular surface positive electrostatic potential is shown in red, while the negative electrostatic potential is shown in blue. As shown in Figure 6 , the Pt-Cl bond is mainly surrounded by the negative electrostatic potential, which means that this region has the ability to contribute electrons and nucleophilic properties. The C-H bond is mainly surrounded by the positive electrostatic potential; thus, this region has the ability to obtain electrons and electrophilic properties. Methods other than electrostatic potential cannot visually display the amphiphilicity of halogen-containing systems.

We used Multiwfn 3.8 to draw electrostatic potential contour maps of the three complexes in Figure 7 . The black solid line and the dashed line in this figure represent the regions where the electrostatic potential is positive and negative, respectively. The bold blue line corresponds to the vdW surface (isosurface of electron density = 0.001 a.u., as defined by R. F. W. Bader). From the graph, it is clear that the Pt atom is overall positively charged, because the vdW surface close to the Pt atom largely intersects solid contour lines. For the same reason, we can see that Pt(en)Cl₄ has more electrons in Pt and Cl atoms than Pt(bipy)Cl₄ and Pt(dach)Cl₄.

Extreme point information of the molecular surface electrostatic potential (45) of the three complexes are shown in Tables 11 – 13 . The surface electrostatic potential of Pt(bipy)Cl₄ has 2 minimum points (minimum = −2.214701 eV) and 11 maximum points (maximum = 2.434223 eV); Pt(dach)Cl₄ has 5 minimum points (minimum = −2.140967 eV) and 9 maximum points (maximum = 2.275112 eV); Pt(en)Cl₄ has 3 minimum points (minimum = −2.029787 eV) and 8 maximum points (maximum = 2.373782 eV).

The extreme points around each complex are clearly shown in Figure 8 . Red dots represent maximum points and blue dots represent minimum points. In Pt(bipy)Cl₄, the maximum points of the surface electrostatic potential are distributed around the H atom because the electronegativity of the H atom is less than that of the C and N atoms. This is why the H atom in the system shows a positive charge. It can be seen from the position of the two minimum points and the area covered by the atomic sphere that the electrostatic potential of the molecular surface near the Pt and Cl atoms is negative. Therefore, the region of the Pt and Cl atoms is easily attacked by nucleophiles. In Pt(dach)Cl₄ and Pt(en)Cl₄, the region of the H atom connected with the N atom has a larger electrostatic potential and a stronger positive charge. This region leads to weak electronegativity in some parts connected with Pt and Cl atoms. The effect of these parts on the electrostatic potential is not obvious. This explains why the central Pt atom region of Pt(dach)Cl₄ and Pt(en)Cl₄ shows little electrophilicity. Due to the strong tension of the C-C bond, the minimum points of the surface electrostatic potential appear on the molecular surface near the C-C bond in Pt(dach)Cl₄ and Pt(en)Cl₄. Because the ring has a strong tension, the electron density aggregation region between C-C is “squeezed” out to some extent, not completely on the C-C bond. It is the negative contribution of this part of the electron density to the electrostatic potential that produces the minimum electrostatic potential on the molecular surface.

The Multiwfn 3.8 tool is used to analyze the electron-depleted region and the electron-rich region by LOL projection (26, 27). Schmider and Becke first explained that the Localized Orbital Locator (LOL) is a function that is used for locating localized high localization regions (26):

Where τ′(r) (dimensionless variable) is g0(r)/g(r). It always depends on the positive one-electron kinetic energy and is defined as

where Ψi(r) is the Hartree–Fock or the Kohn Sham orbital.

Sason Shaik et al. first defined the charge-shift bonds (46): When the atom binds, the kinetic energy of charge-shift bonds increases sharply and exceeds the reduction of potential energy caused by the reduction of atomic size. If atoms have lone pair electrons, kinetic energy increases more. During bonding, lone pair electrons increase kinetic energy by repulsion between lone pair electrons and bonding electrons. Therefore, the electrons in the bonding region balance the intense motion of the lone pair electrons near the atom by slower fluctuations between atoms. The LOL of Pt(bipy)Cl₄, Pt(dach)Cl₄, and Pt(en)Cl₄ is plotted in Figure 9 . The red color substantially reveals the high electron localization nature in the bonding regions. The degree of electron localization between Pt-Cl and Pt-N is not as high as the case of C-C and C-N bonds; this is a known feature of the “charge-shift bond” (47).

In a specific region, LOL represents the degree (strong or weak) of the limitation of the electronic movement. The shaded surface map with the projection effect of the electron localization function (ELF) of Pt(bipy)Cl₄, Pt(dach)Cl₄, and Pt(en)Cl₄ is plotted in Figure 10 . The high electron depletion region between the valence shell and the inner shell is represented by blue circles around the nucleus. Most of them appear in areas far from Pt atoms. The red-colored area represents the high localized electron regions. In order to stabilize the molecule, the electrons learn to localize on the outer side of the molecule. In Figure 10 , we can see that electrons occupy the outside of the complexes and thus Pt(bipy)Cl₄, Pt(dach)Cl₄, and Pt(en)Cl₄ are stabilized.